Let [Formula: see text] be a congruence subgroup of text]. Using Poincaré series text]-finite matrix coefficients integrable discrete representations text], we construct spanning set for the space Siegel cusp forms weight We prove non-vanishing certain elements this using Muić’s integral criterion on locally compact Hausdorff groups. Moreover, representation theory study Petersson inner product...

Abstract We introduce a holomorphic torsion invariant of log-Enriques surfaces index two with cyclic quotient singularities type $\frac {1}{4}(1,1)$ . The moduli space such k singular points is modular variety orthogonal associated unimodular lattice signature $(2,10-k)$ prove that the invariant, viewed as function variety, given by Petersson norm an explicit Borcherds product. note this essent...

Moduli spaces of hyperbolic surfaces may be endowed with a symplectic structure via the Weil–Petersson form. Mirzakhani proved that Weil–Petersson volumes exhibit polynomial behaviour and that their coefficients store intersection numbers on moduli spaces of curves. In this survey article, we discuss these results as well as some consequences and applications.

We construct a Petersson-Weil type Kähler form on the moduli spaces of Higgs bundles over a compact Kähler manifold. A fiber integral formula for this form is proved, from which it follows that the Petersson-Weil form is the curvature of a certain determinant line bundle, equipped with a Quillen metric, on the moduli space of Higgs bundles over a projective manifold. The curvature of the Peters...

Geodesic completness and self-adjointness imply that the Hamiltonian for anyons is the Laplacian with respect to the Weil-Petersson metric. This metric is complete on the DeligneMumford compactification of moduli (configuration) space. The structure of this compactification fixes the possible anyon configurations. This allows us to identify anyons with singularities (elliptic points with ramifi...

The Rankin-Selberg convolution is usually normalized by the multiplication of a zeta factor. One naturally expects that the non-normalized convolution will have poles where the zeta factor has zeros, and that these poles will have the same order as the zeros of the zeta factor. However, this will only happen if the normalized convolution does not vanish at the zeros of the zeta factor. In this ...

this paper is an investigation of $l$-dual frames with respect to a function-valued inner product, the so called $l$-bracket product on $l^{2}(g)$, where g is a locally compact abelian group with a uniform lattice $l$. we show that several well known theorems for dual frames and dual riesz bases in a hilbert space remain valid for $l$-dual frames and $l$-dual riesz bases in $l^{2}(g)$.